A pan filled with hot food cools from 94∘C to 86∘C in 2 minutes. When the room temperature is 20∘C. How long will it cool from 74∘C to 66∘C?
2 minutes
1.8 minutes
2.8 minutes
2.5 minutes
A
1.8 minutes
B
2.5 minutes
C
2 minutes
D
2.8 minutes
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Solution
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Using Newton's law of cooling with approximation, dTdt=−kms(Tavg−Ts)
Case 1 : dt=2 minutes; Ts=20
Tavg=94+862=90 and dT=94−86=8
∴−kms=dTdt.1Tavg−Ts=82×70=0.05714 .......(a)
Case 2 : Ts=20
Tavg=74+662=70 and dT=74−66=8
∴ Time in which it cools down 8dt=0.05714×(70−20)
⟹dt=2.8 minutes
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